Because circular objects are projected to ellipses in images, ellipse fitting is a first step for 3-D analysis of circular objects in computer vision applications. For this reason, the study of ellipse fitting began as soon as computers came into use for image analysis in the 1970s, but it is only recently that optimal computation techniques based on the statistical properties of noise were established. These include renormalization (1993), which was then improved as FNS (2000) and HEIV (2000). Later, further improvements, called hyperaccurate correction (2006), HyperLS (2009), and hyper-renormalization (2012), were presented. Today, these are regarded as the most accurate fitting methods among all known techniques. This book describes these algorithms as well implementation details and applications to 3-D scene analysis.

We also present general mathematical theories of statistical optimization underlying all ellipse fitting algorithms, including rigorous covariance and bias analyses and the theoretical accuracy limit. The results can be directly applied to other computer vision tasks including computing fundamental matrices and homographies between images.

This book can serve not simply as a reference of ellipse fitting algorithms for researchers, but also as learning material for beginners who want to start computer vision research. The sample program codes are downloadable from the website: https://sites.google.com/a/morganclaypool.com/ellipse-fitting-for-computer-vision-implementation-and-applications.

About the Author(s)

Kenichi Kanatani , Okayama UniversityKenichi Kanatani received his B.E., M.S., and Ph.D. in applied mathematics from the University of Tokyo in 1972, 1974, and 1979, respectively. After serving as Professor of computer science at Gunma University, Gunma, Japan, and Okayama University, Okayama, Japan, he retired in 2013 and is now Professor Emeritus of Okayama University. He was a visiting researcher at the University of Maryland, U.S., (1985-1986, 1988-1989, 1992), the University of Copenhagen, Denmark (1988), the University of Oxford, U.K. (1991), INRIA at Rhone Alpes, France (1988), ETH, Switzerland (2013), University of Paris-Est, France (2014), and Linkoping University, Sweden (2015). He is the author of K. Kanatani, Group-Theoretical Methods in Image Understanding (Springer, 1990), K. Kanatani, Geometric Computation for Machine Vision (Oxford University Press, 1993), K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice (Elsevier, 1996; reprinted Dover, 2005), and K. Kanatani, Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics (AK Peters/CRC Press 2015). He received many awards including the best paper awards from IPSJ (1987), IEICE (2005), and PSIVT (2009). He is a Fellow of IEICE and IEEE.

Yasuyuki Sugaya , Toyohashi University of TechnologyYasuyuki Sugaya received his B.E., M.S., and Ph.D. in computer science from the University of Tsukuba, Ibaraki, Japan, in 1996, 1998, and 2001, respectively. After serving as Assistant Professor of computer science at Okayama University, Okayama, Japan, he is currently Associate Professor of computer science and engineering at Toyohashi University of Technology, Toyohashi, Aichi, Japan. His research interests include image processing and computer vision. He received the IEICE best paper award in 2005.

Yasushi Kanazawa, Toyohashi University of TechnologyYasushi Kanazawa received his B.E. and M.S. degree in information engineering from Toyohashi University of Technology in 1985 and 1987, respectively, and his Ph.D in information and computer science from Osaka University in 1997. After engaging in research and development of image processing systems at Fuji Electric Co., Tokyo, Japan, and serving as Lecturer of Information and Computer Engineering at Gunma College of Technology, Gunma, Japan, he is currently Associate Professor of computer science and engineering at Toyohashi University of Technology, Aichi, Japan. His research interests include image processing and computer vision.